Pen testing is the problem of selecting high-capacity resources when the only way to measure the capacity of a resource expends its capacity. We have a set of $n$ pens with unknown amounts of ink and our goal is to select a feasible subset of pens maximizing the total ink in them. We are allowed to gather more information by writing with them, but this uses up ink that was previously in the pens. Algorithms are evaluated against the standard benchmark, i.e, the optimal pen testing algorithm, and the omniscient benchmark, i.e, the optimal selection if the quantity of ink in the pens are known. We identify optimal and near optimal pen testing algorithms by drawing analogues to auction theoretic frameworks of deferred-acceptance auctions and virtual values. Our framework allows the conversion of any near optimal deferred-acceptance mechanism into a near optimal pen testing algorithm. Moreover, these algorithms guarantee an additional overhead of at most $(1+o(1)) \ln n$ in the approximation factor of the omniscient benchmark. We use this framework to give pen testing algorithms for various combinatorial constraints like matroid, knapsack, and general downward-closed constraints and also for online environments.

翻译：笔测试是一个资源选择问题，其中测量资源容量的唯一方式会消耗该容量。我们有一组$n$支未知墨水量的笔，目标是选择一个可行的子集，最大化其中所含的总墨水量。我们可以通过书写来获取更多信息，但这会消耗笔中已有的墨水。算法根据标准基准（即最优笔测试算法）和全知基准（即已知笔中墨水量时的最优选择）进行评估。我们通过类比延迟接受拍卖和虚拟价值的拍卖理论框架，识别出最优和近似最优的笔测试算法。我们的框架允许将任何近似最优的延迟接受机制转化为近似最优的笔测试算法。此外，这些算法保证在全知基准的近似因子中额外开销最多为$(1+o(1)) \ln n$。我们利用这一框架，为各种组合约束（如拟阵、背包和一般向下封闭约束）及在线环境提供了笔测试算法。